22+q=1/2q

Solution for 22+q=1/2q equation:

22+q=1/2q

We move all terms to the left:

22+q-(1/2q)=0


Domain of the equation: 2q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

q-(+1/2q)+22=0

We get rid of parentheses

q-1/2q+22=0

We multiply all the terms by the denominator


q*2q+22*2q-1=0

Wy multiply elements

2q^2+44q-1=0

a = 2; b = 44; c = -1;
Δ = b2-4ac
Δ = 442-4·2·(-1)
Δ = 1944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-18\sqrt{6}}{2*2}=\frac{-44-18\sqrt{6}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+18\sqrt{6}}{2*2}=\frac{-44+18\sqrt{6}}{4}
$